DeepM&Mnet for hypersonics: Predicting the coupled flow and finite-rate chemistry behind a normal shock using neural-network approximation of operators

In high-speed flow past a normal shock, the fluid temperature rises rapidly triggering downstream chemical dissociation reactions. The chemical changes lead to appreciable changes in fluid properties, and these coupled multiphysics and the resulting multiscale dynamics are challenging to resolve numerically. Using conventional computational fluid dynamics (CFD) requires excessive computing cost. Here, we propose a totally new efficient approach, assuming that some sparse measurements of the state variables are available that can be seamlessly integrated in the simulation algorithm. We employ a special neural network for approximating nonlinear operators, the DeepONet, which is used to predict separately each individual field, given inputs from the rest of the fields of the coupled multiphysics system. We demonstrate the effectiveness of DeepONet by predicting five species in the non-equilibrium chemistry downstream of a normal shock at high Mach numbers as well as the velocity and temperature fields. We show that upon training, DeepONets can be over five orders of magnitude faster than the CFD solver employed to generate the training data and yield good accuracy for unseen Mach numbers within the range of training. Outside this range, DeepONet can still predict accurately and fast if a few sparse measurements are available. We then propose a composite supervised neural network, DeepM&Mnet, that uses multiple pre-trained DeepONets as building blocks and scattered measurements to infer the set of all seven fields in the entire domain of interest. Two DeepM&Mnet architectures are tested, and we demonstrate the accuracy and capacity for efficient data assimilation. DeepM&Mnet is simple and general: it can be employed to construct complex multiphysics and multiscale models and assimilate sparse measurements using pre-trained DeepONets in a "plug-and-play" mode.Comment: 30 pages, 17 figure

Verification of a fluid-dynamics solver using correlations with linear stability results

A novel method is described for verification of fluid-dynamics solvers based on correlations with solutions from linear stability analysis. A difficulty with the linear stability analysis solutions for spatially developing flows is that flow fields typically exhibit exponentially growing features compromising the performance of classical error metrics. This motivates the construction of a projection-based metric that only assumes the shape of the solution and not the growth rate of the perturbations, thus also allowing the latter to be determined. The proposed correlation metric complements classical error metrics, such as p-norms, and can also be used for time-dependent problems with realistic boundary conditions. We demonstrate how the present method can be applied in the verification of an Euler solver for the instability behavior of laminar compressible free and confined shear layers

Verification of a fluid-dynamics solver using correlations with linear stability results

A novel method is described for verification of fluid-dynamics solvers based on correlations with solutions from linear stability analysis. A difficulty with the linear stability analysis solutions for spatially developing flows is that flow fields typically exhibit exponentially growing features compromising the performance of classical error metrics. This motivates the construction of a projection-based metric that only assumes the shape of the solution and not the growth rate of the perturbations, thus also allowing the latter to be determined. The proposed correlation metric complements classical error metrics, such as p-norms, and can also be used for time-dependent problems with realistic boundary conditions. We demonstrate how the present method can be applied in the verification of an Euler solver for the instability behavior of laminar compressible free and confined shear layers